103 



9 9 



where c varies from t . 1j or — . a down to zero, and d varies from a or b 



down to — . b or . a. Solving the ten equations for the ten ditferent 



values of f and a, we get the following table: 



No.... 1 2 3 4 5 6 7 8 9 10 



a .958 .875 .800 .726 .6«4 .611 .566 .535 .512 .502 



f .042 .126 .216 .315 .424 .556 .716 .935 1.24 2.07 



Table I. 

 It will be seen from the table by countiiiLC the divisions from A as 1. 2. 3. 

 etc., that nearly half the water flows through the first three divisions 

 and that there is a gradual decrease toward B. The relative value of f 

 from the different divisions shows a very slight tlowage from the iirst 

 division with a rapid increase from each of the succeeding divisions until 

 the two lower divisions at 1) carry off one-half of the amount aljsorbed. 

 This shows in a very vivid way the pnmounced effect of gravity or any 

 constant external force upon a liquid. The amount going in along A B is 

 of course eciual to the amount flowing out along A D. since the equation 

 of continuity must hold true. 



It is interesting to note that the curve given by plotting the tlowage 

 from A D is very nearly a tractrix or antifriction curve. See Fig. 3. It 

 would undouldedly be an exact tractrix had the number of divisions of 

 A D been taken small enough, i. e., if twenty or thirty equal divisions had 

 been taken Instead of ten. 



In Fig. 3 the line O X corresponds to the distance A D in Fig. 1, and 

 the y-coordinates of the curve are given by the values f taken from 

 'j.able I. 



Fig. 4 shows the distribution of absorption into the area A B C D 

 along A B, the line A B of the figure corresponding to the line -x B of the 

 area. The y-coordinates of the cui've being taken from Table I as the 

 different values of a. 



Figs. 3 and 4 then show the distribution of absorption ana flowage 

 along A B and A D. 



E'xtending this method by taking A B one hundred and keeping A D 

 ten, we get approximately an artesian well area. The values of f and a 

 for this case are given below: 



6 7 8 9 10 



005 



.616 .762 .981 1.82 2.53 



